You Can’t Smooth the Big Bang

As a kid, I was fascinated by cosmology. I wanted to know how the universe began, possibly disproving gods along the way, and I gobbled up anything that hinted at the answer.

At the time, I had to be content with vague slogans. As I learned more, I could match the slogans to the physics, to see what phrases like “the Big Bang” actually meant. A large part of why I went into string theory was to figure out what all those documentaries are actually about.

In the end, I didn’t end up working on cosmology due my ignorance of a few key facts while in college (mostly, who Vilenkin was). Thus, while I could match some of the old popularization stories to the science, there were a few I never really understood. In particular, there were two claims I never quite saw fleshed out: “The universe emerged from nothing via quantum tunneling” and “According to Hawking, the big bang was not a singularity, but a smooth change with no true beginning.”

As a result, I’m delighted that I’ve recently learned the physics behind these claims, in the context of a spirited take-down of both by Perimeter’s Director Neil Turok.

neil20turok_cropped_photo20credit20jens20langen

My boss

Neil held a surprise string group meeting this week to discuss the paper I linked above, “No smooth beginning for spacetime” with Job Feldbrugge and Jean-Luc Lehners, as well as earlier work with Steffen Gielen. In it, he talked about problems in the two proposals I mentioned: Hawking’s suggestion that the big bang was smooth with no true beginning (really, the Hartle-Hawking no boundary proposal) and the idea that the universe emerged from nothing via quantum tunneling (really, Vilenkin’s tunneling from nothing proposal).

In popularization-speak, these two proposals sound completely different. In reality, though, they’re quite similar (and as Neil argues, they end up amounting to the same thing). I’ll steal a picture from his paper to illustrate:

neilpaperpic

The picture on the left depicts the universe under the Hartle-Hawking proposal, with time increasing upwards on the page. As the universe gets older, it looks like the expanding (de Sitter) universe we live in. At the beginning, though, there’s a cap, one on which time ends up being treated not in the usual way (Lorentzian space) but on the same footing as the other dimensions (Euclidean space). This lets space be smooth, rather than bunching up in a big bang singularity. After treating time in this way the result is reinterpreted (via a quantum field theory trick called Wick rotation) as part of normal space-time.

What’s the connection to Vilenkin’s tunneling picture? Well, when we talk about quantum tunneling, we also end up describing it with Euclidean space. Saying that the universe tunneled from nothing and saying it has a Euclidean “cap” then end up being closely related claims.

Before Neil’s work these two proposals weren’t thought of as the same because they were thought to give different results. What Neil is arguing is that this is due to a fundamental mistake on Hartle and Hawking’s part. Specifically, Neil is arguing that the Wick rotation trick that Hartle and Hawking used doesn’t work in this context, when you’re trying to calculate small quantum corrections for gravity. In normal quantum field theory, it’s often easier to go to Euclidean space and use Wick rotation, but for quantum gravity Neil is arguing that this technique stops being rigorous. Instead, you should stay in Lorentzian space, and use a more powerful mathematical technique called Picard-Lefschetz theory.

Using this technique, Neil found that Hartle and Hawking’s nicely behaved result was mistaken, and the real result of what Hartle and Hawking were proposing looks more like Vilenkin’s tunneling proposal.

Neil then tried to see what happens when there’s some small perturbation from a perfect de Sitter universe. In general in physics if you want to trust a result it ought to be stable: small changes should stay small. Otherwise, you’re not really starting from the right point, and you should instead be looking at wherever the changes end up taking you. What Neil found was that the Hartle-Hawking and Vilenkin proposals weren’t stable. If you start with a small wiggle in your no-boundary universe you get, not the purple middle drawing with small wiggles, but the red one with wiggles that rapidly grow unstable. The implication is that the Hartle-Hawking and Vilenkin proposals aren’t just secretly the same, they also both can’t be the stable state of the universe.

Neil argues that this problem is quite general, and happens under the following conditions:

  1. A universe that begins smoothly and semi-classically (where quantum corrections are small) with no sharp boundary,
  2. with a positive cosmological constant (the de Sitter universe mentioned earlier),
  3. under which the universe expands many times, allowing the small fluctuations to grow large.

If the universe avoids one of those conditions (maybe the cosmological constant changes in the future and the universe stops expanding, for example) then you might be able to avoid Neil’s argument. But if not, you can’t have a smooth semi-classical beginning and still have a stable universe.

Now, no debate in physics ends just like that. Hartle (and collaborators) don’t disagree with Neil’s insistence on Picard-Lefschetz theory, but they argue there’s still a way to make their proposal work. Neil mentioned at the group meeting that he thinks even the new version of Hartle’s proposal doesn’t solve the problem, he’s been working out the calculation with his collaborators to make sure.

Often, one hears about an idea from science popularization and then it never gets mentioned again. The public hears about a zoo of proposals without ever knowing which ones worked out. I think child-me would appreciate hearing what happened to Hawking’s proposal for a universe with no boundary, and to Vilenkin’s proposal for a universe emerging from nothing. Adult-me certainly does. I hope you do too.

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14 thoughts on “You Can’t Smooth the Big Bang

  1. Lubos Motl

    What? Do you say he claims that there is a general problem with Hartle-Hawking? If the article above is supposed to contain evidence, I didn’t understand a word of it. It sounds like utter rubbish emitted by someone who has no clue.

    Hartle-Hawking is just the claim that one may calculate a preferred wave function on a slice that can be continuously connected to a point in the Euclidean spacetime signature. This has really nothing to do with the singular character of the Big Bang – the HH state is calculable even at finite radius of the Universe.

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    1. 4gravitonsandagradstudent Post author

      He’s claiming the wavefunction Hartle and Hawking calculated in the context of the no-boundary proposal is incorrect. The paper linked is the most recent one, which covers the instability claims, this older paper has more details of the calculation and focuses on the claim that the Hartle-Hawking wavefunction is mistaken. As I mentioned in the post, Hartle does seem to take the substance of the criticism seriously, and is defending the HH wavefunction by arguing that you can still get it out of Picard-Lefschetz, not that the Euclidean procedure is correct.

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        1. Lubos Motl

          Thanks for your answer. The word “incorrect” simply sounds tendentious or unjustified. Turok et al. seem to be fighting against a straw man – their own version of what the “candidate” should be. But to disprove an idea formulated without all the details, one has to exclude all possibilities what the details could be, right?

          I think that you unambiguously misrepresent the claims in the newest paper by Hartle et al. They don’t say that the Euclidean calculation is incorrect. Instead, they do a calculation of the Picard-Lefschetz method that exactly reproduces the result obtained using the Euclidean signature, see comments e.g. below eqn (2.6) on page 5, so they say that the Turok et al. criticism is completely wrong.

          Your suggestions that someone else except for the authors of Turok et al. have presented any reasons to claim that Turok et al. isn’t just plain wrong seem completely unfounded to me.

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  2. Gary

    “As a kid, I was fascinated by cosmology. I wanted to know how the universe began, possibly disproving gods along the way, and I gobbled up anything that hinted at the answer.”

    This is where you went terribly and utterly wrong. The “universe”—the sum/whole* of existence—is a fact that no amount of reasoning can get behind or beyond. To think of the “universe” as a whole is an impossibility; while to talk of its origin is to assume, first, that there is such a bounded entity called “universe”, which could be conceived by our mammalian brains, and, second, that it did “originate”. The anthropocentric delusion which underlies the assumption of an “origin” of the “universe” comes from an incredibly stupid ANALOGY. We, 2-footed mammals, know that we are born and die, so we try to project our imaginations/fantasies to the world. (This is what E.Jaynes called Mind Projection Fallacy)

    Regarding your comment that a “beginning” for “universe” disproves gods, it is a flabbergasting non sequitur. Witches/goblins/dragons/demons/angels/elves/ghosts/ gods(deified ghosts) are imaginary creatures invented by primitive savages to explain their experiences. As Edward Tylor said in his “Primitive Culture”, the deepest of all divisions in the history of human thought was that which divided Animism from Materialism. The starting point for this species was the creation by the befogged ignorance of primitive people of that welter of “ghosts” and “gods” to hide their ignorance of the character of nature that leads to the assumption of the existence of “gods”. And this mode of thought continued untill, in ancient Greece, Thales and Democritus, the so-called materialist natural philosophers, laid the foundation stone of Science. In other words, to refute/laugh at Apollo / Zeus / Osiris / Krishna / Yahweh /Mithra/Christ/Adonis/Attis/etc. you don’t need to find/invent a “beginning” for “universe”.

    Now, about the Big Bang. It is at best a hypothesis, and at worst a pernicious myth. This idea , originally, came from Abbe Lemaitrem, a “mathematician” and a moronic Catholic priest, who tried to project Creation Ex Nihilo myth of his primitive cult into “universe”. He did this by identifying the singular point which appears in “some” solutions of Hilber-Einstein equations of general theory of relativity (a penicious misnomer as Vladimir Fock pointed out a long time ago). He also tried to get his “cosmology” called “the primeval atom”. Then came the war which as always produced a surge in “religiosity” and then came the Master propagandist, fame-hungry George Gamov, who popularized and dogmatized thie “Big Bang”. And ever since Gamov, “cosmologists” have tried (like Pythagoreans and Ptolemy) to fit the observational facts to their perfect, a priori “mathematical” models. And every contradiction of the model with observation has been recolved by “inventing” hypothetical entities. In other branches of science, you preceed from observation/experiment to a conclusion, BUT in cosmology they proceed from conclusion to observation.
    Just to give you an example. In most textbooks nowadays you see the statement that Gamov and his collaborators predicted the 2.7 K temperature prior to Penzias and Wilson’s discovery of CBR, while the steady-state theory of Hoyle, Narlikar and Gold did not predict this
    temperature. And Gamov’s prediction of the CBR is “hailed”/”interpreted” as one of the strongest arguments in favour of the Big Bang. However, these two models have one very important aspect in common: both accept the interpretation of the cosmological redshift as being due to a Doppler
    effect, which means that both models accept the expansion of the “universe”. But there is a third model of the “universe” which has been developed by several people including Nernst, Finlay-Freundlich, Max Born and Louis de Broglie. It is based on a “universe” in dynamical
    equilibrium without expansion and without continuous creation of matter. (one out of many models, amother promising one being the A. Logunov’s model based on his Relativistic Theory of Gravitation).

    Gamov tried desperately to convince everybody that he had predicted correctly, and before everyone else, the temperature of the CBR. However, Gamov, Alpher, and Hermann obtained from T » 5 K to T = 50 K in monotonic order (5 K, ³ 5 K, 7 K and 50 K)… These were very poor
    predictions compared with Guillaume, Eddington, Regener and Nernst, McKellar and Herzberg, Finlay-Freundlich and Max Born’s predictions, who arrived at, respectively: 5 K < T < 6 K, T = 3.1 K, T = 2.8 K, T = 2.3 K, 1.9 K < T < 6.0 K!

    All of these people obtained these values from measurement and/or theoretical calculations, but none of them utilized the “Big Bang”. And this shows clearly that the Penzias and Wilson’s discovery of ~3K CBR cannot be considered as “evidence” for the “Big Bang”. Quite the
    contrary, as the models of a “universe” in dynamical equilibrium predicted its value BEFORE Gamow and with better ACCURACY, its discovery could be indicative of a “universe” in dynamical equilibrium.

    But against this and other scientific/observational objections to “Big Bang” hypothesis, it has become a dogma because of the socio-psychological environment of America and Europe, 2 cultures honeycombed by the Jewish mithologies.

    As David Bohm said: “It means a lot to these people (Big Bang devotees) that they are explaining their own origin with the “origin” of the “universe”. That gives them tremendous impetus to do the work”.

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    1. Don Kiddick

      Hi this is the Nobel committee, you’ll be happy to know you have been awarded the very last Nobel Prize in Physics ever awarded. You have single-handedly destroyed the whole field, congratulations, we can all quit now.

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      1. Gary

        Shove that Nobel prize up your ass !

        It’s because of brainless chimps like you that the so-called “revolutions” in (theoretical) physics happen. Witless cunts like you hero-worship previous physicists, dogmatize half-baked hypotheses and after a while, when your idiotic and sacred “models” crumble away, start screaming REVOLUTION, REVOLUTION,….

        FYI, I am an astronomer, a person who does make real OBSERVATIONS. I just mentioned one out of many scientific/observational objections to current mathematical theologian’s ( aka cosmologists’) a priori dogmas. Other people like Geoffrey Burbidge, Mike Disney, Hannes Alfven, Fred Hoyle have also commited sacrilege by criticizing/debunking the Le maitre’s hypothesis, but to no avail.

        Don’t worry!
        Cretinous cunts like you have always existed. People who kept alive delusions like geocentrism, cardiocentric neurophysiology, witchcraft, teligious cults, etc.

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  4. Francis Erdman

    I tried posting the following earlier but WP barfed on me so if this is a duplicate, please accept my apologies and remove it. 🙂

    As a pure amateur enthusiast here (athough with a computer science background and I have read Hawking’s books and did a year physics undergrad so not entirely ignorant hopefully lol) my understanding of the problem is the following. If the quantum state of the Universe (call hat QSU) tunnels from a zero solution of General Relativity into a anti-DeSitter solution (Vilenkin’s view) this produces a universe not smooth enough for galaxies to form. This is because this original result was done using something called Euclidean space and at small scales this does not work anymore, so you have to use Lorentz space to do the calculation, and, doing that, you get no longer a smooth anti-DeSitter solution, but rather a chaotic one, so basically our lovely QSU goes from a zero (or null?) solution to an ADS one not suitable for galaxy formation. Is this about right? (Again, total amatuer here, lol.) Just one very naive thought here – if say the QSU “arrives” at the ADS solution with a radius of something like the Plank Length (10^-31 meters) and for interesting stuff to happen (like inflation, say), you probably want a bit more radius than this (say maybe 10^-18 meters, around the size of a proton). You can always evolve the QSU unitarily from Plank size to Proton size, but then you run (evidently, if I understand correctly) into an ADS situation that is too chaotic for galaxies to form and son on. So, how about this. Who is to say you are limited to our hero the QSU only tunneling once? How about she tunnels N number of times, trying out different ADS solutions, until, at long last, she arrives at an ADS solution (with about a proton or so size radius, enough for inflation) that is nice and smooth the way she has always wanted. Every time she tries out an ADS solution (or, “tunnels”) she has a smaller probability of tunneling again, so the longer this goes on, the fewer times she tunnels, until, at length, she finds a nice, smooth, proton-sized ADS metric, and after that her tunneling probability is very low, so she just stays with that, jugging along uniltarily, until we finally get the universe we see out there in the Hubble telescope. She sort of Newton-Raphson methods her way into the correct ADS solution like finding the root of a function. After all, if she can tunnel once, who is to say she can’t tunnel N times, until she finds what she is looking for. Of course I would not know how to describe that formally, but intuitively it seems reasonable. Cool blog! 🙂

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    1. 4gravitonsandagradstudent Post author

      Glad you enjoyed the blog!

      I get what you’re thinking, but you’ve got a couple misunderstandings:

      First, a minor terminological one: it’s dS space, not AdS. deSitter space is the “spherical” one, it produces a universe with a positive cosmological constant, like ours seems to have. Anti-deSitter has a negative cosmological constant, it’s the “hyperbolic” one. It’s of interest to string theorists because of AdS/CFT, so you might have heard it mentioned more often, but in this context people are talking about dS.

      Second, the issue isn’t that the universe is too small, or too chaotic, under Vilenkin’s setup: the problem is that Vilenkin’s setup isn’t stable. This sounds like the same sort of claim: if it’s unstable, then it would behave chaotically, right? But the important distinction is that here the solutions Vilenkin and Turok are trying to write down aren’t just the universe at one time or another, they’re trying to be descriptions of the whole history of the universe at once, from the Euclidean cap to the distant future. When that kind of description is unstable, it doesn’t mean that it changes over time, because time is already part of the picture. Instead, it means that the setup just doesn’t work, that you can’t end up there to begin with. So it’s not the kind of thing the universe could solve by tunneling again until it finds something stable, if there was a stable picture of the universe that you could tunnel to then it could have tunneled there to start with. What Turok was trying to argue is that the final picture, a history from a tunneling event to a long-lived universe, doesn’t work.

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      1. Francis Erdman

        Thanks for your clarification. I do get DeSitter / anti-DeSitter confused, lol. Yes I think I understand what you are saying, that the Euclidean model is a history of the whole universe from the beginning of time til the end, so such a model would have to be stable. I wonder if you have run across Lee Smolin’s book, “Life of the Universe” that posits a continual creation of worlds via black holes, which serve as ways to “mutate” the laws of physics , so that “successful” worlds are the ones that produce the most black holes – sort of a biological model of cosmogenesis – philosophically appealing, and perhaps a fall-back if the Hartle-Hawking program is not working out. 😉

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